1. How do I solve a proportion?
Proportions
How do I solve a proportion?

2. Proportions – What are they??
Proportions are a way to relate information.
They compare two ratios.

3. Proportions – What are they??
Proportion = a pair of equal ratios ×3 ×3

4. How do we tell if something really is a proportion?
Method 1: Put both sides in lowest terms. ÷5
÷15 ÷5
÷15

5. How do we tell if something really is a proportion?
Method 1: Put both sides in lowest terms.
The fractions are the same, so it is a true proportion.

6. How do we tell if something really is a proportion?
Method 2: Find the cross products.

7. Cross-Product
Multiply the numerator of one ratios by the denominator of the other ratio.
3×2=6
6×1=6

8. The cross products are the same, so it is a true proportion.
If the cross products are equal, the then ratios are equal, and it is a true proportion.
3×2=6
The cross products are the same, so it is a true proportion.
6×1=6

9. Are these proportions equal?
Method 1 – Lowest Terms ÷2 ÷2

10. Are these proportions equal?
Method 1 – Lowest Terms
No – they are not equal!!

11. Are these proportions equal?
Method 2 – Cross Products
8×16=128
9×14=126
No – they are not equal!!

12. Are these proportions equal?
YES – they are equal!!

13. Are these proportions equal?
YES – they are equal!!

14. Are these proportions equal?
No – they are not equal!!

15. Now, let’s try something harder
Sometimes, we will only know 3 of the 4 values in a proportion. The missing value is a VARIABLE. Take a look….
Z is the variable

16. Now, let’s try something harder
When we have a variable, we can still cross-multiply.
10×5 = 50
1×Z = 1Z

17. Now, let’s try something harder
What do you think we are going to do now?
10×5 = 50
1×Z = 1Z
Write the cross products equal to each other.

18. Now, let’s try something harder
What do you think we are going to do now?
50 = 1Z
Write the cross products equal to each other.

19. Now, let’s try something harder
What do you think we are going to do next?
50 = 1Z
It is an equation so we are going to do the inverse - DIVIDE.

20. Now, let’s try something harder
What do you think we are going to do next?
50 = 1Z
50 ÷ Z = 50 so Z = 50
It is an equation so we are going to do the inverse - DIVIDE.

21. Solve for the variable:
Let’s try again
Solve for the variable:
8×15 = 120
4×X = 4X
4X = 120
120÷4=30
so X = 30

22. Here are some steps: 1.) Cross multiply.
2.) Write the cross-products equal to each other.
3.) Divide the number by itself by the number with the variable.
4.) Write your answer as x = …

23. Now You TRY

24. How do I solve a proportion?
Summarize
Answer the EQ:
How do I solve a proportion?